Classical and quantum security analysis via smoothing of Renyi entropy of order 2

It is known that the security evaluation can be done by smoothing of Renyi entropy of order 2 in the classical ans quantum settings when we apply universal2 hash functions. This fact can be extended to the case when we apply epsilon-almost dual universal2 hash functions. Demonstrating the smoothing of Renyi entropy of order 2, we derived security bounds for universal composability and mutual information criterion under the condition in the classical and quantum setting. Further, we apply this analysis to the secret key generation with error correction.